{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Theoretical framework of liquidity provision by financial intermediaries, namely banks and mutual funds. It is build upon the model of Diamond and Dybvig (1983), to examine how different types of contracts impact the provision of liquidity by financial intermediaries.\n",
    "\n",
    "- **Types of Contracts:** The paper considers bank deposits, which are debt contracts, and mutual fund shares, which are equity contracts. The mutual funds may or may not use swing pricing to adjust their Net Asset Value (NAV). The banks may or may not have bank insurance.\n",
    "\n",
    "- **Aims:** To compare liquidity constraints under different contractual forms and provide a unified measure of liquidity provision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Time and Economy Structure: There are three periods.\n",
    "- $t=0$ : Initial investment decision time.\n",
    "- $t=1$ : Idiosyncratic shock realization and decision time for agents (whether to continue or exit).\n",
    "- $t=2$ : The final period when long-term assets mature and payoffs occur.\n",
    "2. Agents:\n",
    "- There's a continuum of agents who initially have identical endowments.\n",
    "- These agents will experience an idiosyncratic shock at $t=1$ that determines their consumption preference for $t=1$ or $t=2$.\n",
    "3. Assets:\n",
    "- Cash: Every agent is endowed with one unit at $t=0$.\n",
    "- Long-term Asset (\"asset\"): Risky and illiquid, available only for investment at $t=0$ and matures at $t=2$.\n",
    "- Short-term Asset (\"storage\"): Riskless, liquid, and can serve as an alternative to the long-term asset.\n",
    "4. Uncertainty \\& Shocks:\n",
    "- Each agent faces uncertainty about their consumption preference for $t=1$ or $t=2$.\n",
    "- $\\pi$ : Probability an agent is an \"early-type\" and prefers to consume at $t=1$. Essencially captures the size of the idiosyncratic liquidity shock.\n",
    "- $1-\\pi$ : Probability an agent is a \"late-type\" and prefers to consume at $t=2$.\n",
    "- $R$ : Represents the aggregate economic state realized at $t=1$, drawn from a distribution $G(\\cdot)$, with a support of $[1,+\\infty)$. This affects the value of long-term investments.\n",
    "- The realization of $R$ at $t=1$ gives agents and the intermediary a sense of how the economy is performing, which in turn influences decisions about early liquidations or continued investments.\n",
    "5. Long-term Asset Details:\n",
    "- Investing one unit at $t=0$ yields $R$ units at $t=2$.\n",
    "- The asset has value $\\beta(R)$ at $t=1$ if not traded.\n",
    "- Liquidation at $t=1$ incurs a cost $\\phi$, making its value $(1-\\phi) \\beta(R)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import quad\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LPI_Simulation(q, q_b, pi, phi, lam):\n",
    "    gamma=1.5 # utility curvature\n",
    "    maxr = np.inf # maximum return\n",
    "    \n",
    "    # utility function\n",
    "    def u(c): \n",
    "        if c==0:\n",
    "            return -np.inf\n",
    "        else:\n",
    "            return c**(1-gamma)/(1-gamma)\n",
    "    \n",
    "    # fundamentals: exponential distribution\n",
    "    def g(r):\n",
    "        return lam*np.exp(-lam*(r-1))\n",
    "\n",
    "    # beta function:\n",
    "    def beta(r):\n",
    "        return (1+r)/2\n",
    "    \n",
    "    # swing pricing\n",
    "    def c1s(r): # consumption at time 1 if leave\n",
    "        if pi<=x/(x+y*beta(r)):\n",
    "            return x+y*beta(r)\n",
    "        else:\n",
    "            return (x+(1-phi)*y*beta(r))/(1-phi*(1-pi))\n",
    "\n",
    "    def c2s(r): # consumption at time 2 if not leave\n",
    "        if pi<=x/(x+y*beta(r)):\n",
    "            return c1s(r)+y*(r-beta(r))/(1-pi)\n",
    "        else:\n",
    "            return (x+(1-phi)*y*beta(r))*r/((1-phi*(1-pi))*beta(r))\n",
    "    \n",
    "    # mutual funds\n",
    "    def c1f(r): # consumption at time 1 if leave\n",
    "        if pi<=(x+(1-phi)*y*beta(r))/(x+y*beta(r)):\n",
    "            return x+y*beta(r)\n",
    "        else:\n",
    "            return x+(1-phi)*beta(r)*y\n",
    "\n",
    "    def c2f(r): # consumption at time 2 if not leave\n",
    "        if pi<=x/(x+y*beta(r)):\n",
    "            return (x+y*r-pi*c1f(r))/(1-pi)\n",
    "        elif pi<=(x+(1-phi)*y*beta(r))/(x+y*beta(r)):\n",
    "            return (y-(pi*c1f(r)-x)/((1-phi)*beta(r)))*r/(1-pi)\n",
    "        else:\n",
    "            return 0\n",
    "        \n",
    "    # bank\n",
    "    def c1b(r): # consumption at time 1 if leave\n",
    "        if pi<=(x+(1-phi)*y*beta(r))/cb:\n",
    "            return cb\n",
    "        else:\n",
    "            return x+(1-phi)*beta(r)*y\n",
    "\n",
    "    def c2b(r): # consumption at time 2 if not leave\n",
    "        if pi<=x/cb:\n",
    "            return (x+y*r-pi*cb)/(1-pi)\n",
    "        elif pi<=(x+(1-phi)*y*beta(r))/cb:\n",
    "            return (y-(pi*cb-x)/((1-phi)*beta(r)))*r/(1-pi)\n",
    "        else:\n",
    "            return 0\n",
    "    \n",
    "    # bank with diposit insurance\n",
    "    def c1b_ds(r): # consumption at time 1 if leave\n",
    "        if pi<=(x+(1-phi)*y*beta(r))/cb:\n",
    "            return cb\n",
    "        else:\n",
    "            return x+(1-phi)*beta(r)*y\n",
    "\n",
    "    def c2b_ds(r): # consumption at time 2 if not leave\n",
    "        if pi<=x/cb:\n",
    "            return (x+y*r-pi*cb)/(1-pi)\n",
    "        elif pi<=(x+(1-phi)*y*beta(r))/cb:\n",
    "            return (y-(pi*cb-x)/((1-phi)*beta(r)))*r/(1-pi)\n",
    "        else:\n",
    "            return 0\n",
    "    \n",
    "    def cal_cb(r): # function to calculate bank asset value\n",
    "        return g(r)*beta(r)\n",
    "    \n",
    "    # welfare\n",
    "    def swing(r):\n",
    "        return g(r)*(pi*u(c1s(r))+(1-pi)*u(c2s(r)))\n",
    "\n",
    "    def fund(r):\n",
    "        return g(r)*((1-q)*(pi*u(c1f(r))+(1-pi)*u(c2f(r)))+q*u(x+(1-phi)*y*beta(r)))\n",
    "\n",
    "    def bank(r):\n",
    "        return g(r)*((1-q_b)*(pi*u(c1b(r))+(1-pi)*u(c2b(r)))+q_b*u(x+(1-phi)*y*beta(r)))\n",
    "    \n",
    "    def bank_ds(r):\n",
    "        return g(r)*(pi*u(c1b_ds(r))+(1-pi)*u(c2b_ds(r)))\n",
    "    \n",
    "    # optimization problem at time 0\n",
    "    s = np.array([])\n",
    "    f = np.array([])\n",
    "    b = np.array([])\n",
    "    b_ds = np.array([])\n",
    "    expected = quad(cal_cb, 1, np.inf)[0]\n",
    "    \n",
    "    for x in np.linspace(0, 1, 1000):\n",
    "        y = 1 - x\n",
    "        cb = x + y * expected\n",
    "        result = quad(swing, 1, maxr)[0]\n",
    "        s = np.append(s, result)\n",
    "        result = quad(fund, 1, maxr)[0]\n",
    "        f = np.append(f, result)\n",
    "        result = quad(bank, 1, maxr)[0]\n",
    "        b = np.append(b, result)\n",
    "        result = quad(bank_ds, 1, maxr)[0]\n",
    "        b_ds = np.append(b_ds, result)\n",
    "        \n",
    "    argmax_s = np.argmax(s)\n",
    "    argmax_f = np.argmax(f)\n",
    "    argmax_b = np.argmax(b)\n",
    "    argmax_b_ds = np.argmax(b_ds)\n",
    "    \n",
    "    x_s = argmax_s / 1000\n",
    "    x_f = argmax_f / 1000\n",
    "    x_b = argmax_b / 1000\n",
    "    x_b_ds = argmax_b_ds / 1000\n",
    "    y_s = 1 - x_s\n",
    "    y_f = 1 - x_f\n",
    "    y_b = 1 - x_b\n",
    "    y_b_ds = 1 - x_b_ds\n",
    "    cb=x_b+(1-x_b)*expected\n",
    "    cb_ds=x_b_ds+(1-x_b_ds)*expected\n",
    "    \n",
    "    # function to calculate expected LPI\n",
    "    def swing_lpi(r):\n",
    "        if pi<=x_s/(x_s+y_s*beta(r)):\n",
    "            return g(r)*((x_s+y_s*beta(r))/(x_s+(1-phi)*y_s*beta(r))-1)\n",
    "        else:\n",
    "            return g(r)*(((x_s+(1-phi)*y_s*beta(r))/(1-phi*(1-pi)))/(x_s+(1-phi)*y_s*beta(r))-1)\n",
    "\n",
    "    def fund_lpi(r):\n",
    "        if pi<=(x_f+(1-phi)*y_f*beta(r))/(x_f+y_f*beta(r)):\n",
    "            return g(r)*((x_f+y_f*beta(r))/(x_f+(1-phi)*y_f*beta(r))-1)\n",
    "        else:\n",
    "            return g(r)*((x_f+(1-phi)*beta(r)*y_f)/(x_f+(1-phi)*y_f*beta(r))-1)\n",
    "    \n",
    "    def bank_lpi(r):\n",
    "        if pi<=(x_b+(1-phi)*y_b*beta(r))/cb:\n",
    "            return g(r)*(cb/(x_b+(1-phi)*y_b*beta(r))-1)\n",
    "        else:\n",
    "            return g(r)*((x_b+(1-phi)*beta(r)*y_b)/(x_b+(1-phi)*y_b*beta(r))-1)\n",
    "        \n",
    "    def bank_ds_lpi(r):\n",
    "        if pi<=(x_b_ds+(1-phi)*y_b_ds*beta(r))/cb_ds:\n",
    "            return g(r)*(cb_ds/(x_b_ds+(1-phi)*y_b_ds*beta(r))-1)\n",
    "        else:\n",
    "            return g(r)*((x_b_ds+(1-phi)*beta(r)*y_b_ds)/(x_b_ds+(1-phi)*y_b_ds*beta(r))-1)\n",
    "        \n",
    "    # expected LPI\n",
    "    lpi_s= quad(swing_lpi, 1, maxr)[0]\n",
    "    lpi_f= quad(fund_lpi, 1, maxr)[0]\n",
    "    lpi_b= quad(bank_lpi, 1, maxr)[0]\n",
    "    lpi_b_ds= quad(bank_ds_lpi, 1, maxr)[0]\n",
    "    \n",
    "    return x_s, x_f, x_b, x_b_ds, cb, cb_ds, y_s, y_f, y_b, y_b_ds, lpi_s, lpi_f, lpi_b, lpi_b_ds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_VS_Phi_update_three_LPI(q, q_b, pi, lam, phi_values):\n",
    "\n",
    "    # Store the results\n",
    "    xs_values = []\n",
    "    xf_values = []\n",
    "    xb_values = []\n",
    "    xb_ds_values = []\n",
    "    ys_values = []\n",
    "    yf_values = []\n",
    "    yb_values = []\n",
    "    yb_ds_values = []\n",
    "    lpi_s_values = []\n",
    "    lpi_f_values = []\n",
    "    lpi_b_values = []\n",
    "    lpi_b_ds_values = []\n",
    "\n",
    "    for phi in tqdm(phi_values, desc=\"Calculating\"):\n",
    "        x_s, x_f, x_b, x_b_ds, cb, cb_ds, y_s, y_f, y_b, y_b_ds, lpi_s, lpi_f, lpi_b, lpi_b_ds = LPI_Simulation(q, q_b, pi, phi, lam)\n",
    "        xs_values.append(x_s)\n",
    "        xf_values.append(x_f)\n",
    "        xb_values.append(x_b)\n",
    "        xb_ds_values.append(x_b_ds)\n",
    "        ys_values.append(y_s)\n",
    "        yf_values.append(y_f)\n",
    "        yb_values.append(y_b)\n",
    "        yb_ds_values.append(y_b_ds)\n",
    "        lpi_s_values.append(lpi_s)\n",
    "        lpi_f_values.append(lpi_f)\n",
    "        lpi_b_values.append(lpi_b)\n",
    "        lpi_b_ds_values.append(lpi_b_ds)\n",
    "\n",
    "    # Plotting\n",
    "    plt.figure(figsize=(7.5, 5))\n",
    "\n",
    "    plt.plot(phi_values, lpi_f_values, label='Fund equity', color = 'r')\n",
    "    plt.plot(phi_values, lpi_b_values, label='Bank debt', color = 'Black')\n",
    "    plt.plot(phi_values, lpi_b_ds_values, label='Bank debt w/ deposit insurance', color = 'Black', linestyle = 'dashed')\n",
    "    plt.xlabel('$\\phi$')\n",
    "    plt.ylabel('Expected LPI')\n",
    "    # plt.title('Expected LPI vs $\\phi$')\n",
    "    plt.legend()\n",
    "    \n",
    "    plt.savefig('LPI_numerical_three_LPI.eps')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating: 100%|████████████████████████████| 100/100 [02:16<00:00,  1.36s/it]\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_VS_Phi_update_three_LPI(q = 0.3, q_b = 0.3, pi = 0.3, lam = 5, phi_values = np.linspace(0.15, 0.35, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_VS_Phi_update_three_portfolio(q, q_b, pi, lam, phi_values):\n",
    "\n",
    "    # Store the results\n",
    "    xs_values = []\n",
    "    xf_values = []\n",
    "    xb_values = []\n",
    "    xb_ds_values = []\n",
    "    ys_values = []\n",
    "    yf_values = []\n",
    "    yb_values = []\n",
    "    yb_ds_values = []\n",
    "    lpi_s_values = []\n",
    "    lpi_f_values = []\n",
    "    lpi_b_values = []\n",
    "    lpi_b_ds_values = []\n",
    "\n",
    "    for phi in tqdm(phi_values, desc=\"Calculating\"):\n",
    "        x_s, x_f, x_b, x_b_ds, cb, cb_ds, y_s, y_f, y_b, y_b_ds, lpi_s, lpi_f, lpi_b, lpi_b_ds = LPI_Simulation(q, q_b, pi, phi, lam)\n",
    "        xs_values.append(x_s)\n",
    "        xf_values.append(x_f)\n",
    "        xb_values.append(x_b)\n",
    "        xb_ds_values.append(x_b_ds)\n",
    "        ys_values.append(y_s)\n",
    "        yf_values.append(y_f)\n",
    "        yb_values.append(y_b)\n",
    "        yb_ds_values.append(y_b_ds)\n",
    "        lpi_s_values.append(lpi_s)\n",
    "        lpi_f_values.append(lpi_f)\n",
    "        lpi_b_values.append(lpi_b)\n",
    "        lpi_b_ds_values.append(lpi_b_ds)\n",
    "\n",
    "    # Plotting\n",
    "    plt.figure(figsize=(7.5, 5))\n",
    "\n",
    "    plt.plot(phi_values, yf_values, label='Fund equity', color = 'r')\n",
    "    plt.plot(phi_values, yb_values, label='Bank debt', color = 'Black')\n",
    "    plt.plot(phi_values, yb_ds_values, label='Bank debt w/ deposit insurance', color = 'Black', linestyle = 'dashed')\n",
    "    plt.xlabel('$\\phi$')\n",
    "    plt.ylabel('Share of illiquid asset')\n",
    "    # plt.title('Share of illiquid asset vs $\\phi$')\n",
    "    plt.legend()\n",
    "    \n",
    "    plt.savefig('LPI_numerical_three_portfolio.eps')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating: 100%|████████████████████████████| 100/100 [02:13<00:00,  1.34s/it]\n",
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_VS_Phi_update_three_portfolio(q = 0.3, q_b = 0.3, pi = 0.3, lam = 5, phi_values = np.linspace(0.15, 0.35, 100))"
   ]
  }
 ],
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